Finite Group Databasebeta

← #28488331

Subgroups — #28488331

Order 15104.

402 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837752C211yesmaximal, characteristic
2#21425085C211yesmaximal, characteristic
3#21422851C211yesmaximal, characteristic
4#21422782C211yesmaximal, characteristic
5#21422777C211yesmaximal, characteristic
6#21422383C211yesmaximal, characteristic
7C59×#1997C211yesmaximal, characteristic
8C2×#14273727C2211yescharacteristic
9#16837752—22no—
10#16837752—22no—
11#16837455C2211yescharacteristic
12#16837426C2211yescharacteristic
13C2×#14273651C414yes—
14C2×C4×C59⋊C8C2211yescharacteristic
15#16837170—22no—
16#16837152—22no—
17#16837151—22no—
18#16837147—22no—
19#16837124—22no—
20C2×C4⋊Q8×C59C2211yescharacteristic
21C59×#423C2211yescharacteristic
22C4×M16×C59C2211yescharacteristic
23C59×#343—22no—
24C22×Dic118—21no—
25C2×#11745664—21no—
26C22×C59⋊C8C2×C412yes—
27#14273727—21no—
28#14273727—21no—
29#14273727—21no—
30#14273727—21no—
31C2×C4⋊Dic59—21no—
32C2×C4⋊Dic59C2×C412yes—
33C4⋊(C59⋊C8)—21no—
34C4⋊(C59⋊C8)—21no—
35C4⋊(C59⋊C8)D412yes—
36#14273651—28no—
37C22⋊(C59⋊C8)—21no—
38C4×C59⋊C8—21no—
39C4×C59⋊C8D412yes—
40C4×C59⋊C8D412yes—
41C22×Q8×C59C2×C412yes—
42C2×M16×C59—21no—
43C2×M16×C59D412yes—
44C4⋊Q8×C59—21no—
45C4⋊Q8×C59—21no—
46C4⋊Q8×C59—21no—
47C4⋊Q8×C59—21no—
48C2×C4⋊C4×C59—21no—
49C2×C4⋊C4×C59—21no—
50C2×C42×C59C2311yescharacteristic
51C4⋊C8×C59—21no—
52C4⋊C8×C59—21no—
53#97×C59—21no—
54C4×C8×C59—21no—
55C2×Q8×C59—22no—
56C2×Q8×C59—22no—
57C2×Q8×C59—44no—
58C22×C4×C59—22no—
59C22×C4×C59C22×C411yescharacteristic
60C22×C4×C59C2×D411yescharacteristic
61C22×C4×C59#4111yescharacteristic
62C22×Dic59—22no—
63C2×Dic118—41no—
64C2×Dic118—41no—
65C2×Dic118—82no—
66M16×C59—22no—
67M16×C59—22no—
68M16×C59—42no—
69C2×C8×C59—22no—
70C2×C8×C59—41no—
71C4⋊C4×C59—41no—
72C4⋊C4×C59—41no—
73C4⋊C4×C59—41no—
74C4⋊C4×C59—41no—
75C42×C59C2×D411yescharacteristic
76C42×C59C2×D411yescharacteristic
77C42×C59C2×D411yescharacteristic
78C42×C59#4111yescharacteristic
79C4⋊Dic59—22no—
80C4⋊Dic59—22no—
81C4⋊Dic59—41no—
82C4⋊Dic59—41no—
83#11745664—42no—
84C2×C59⋊C8—22no—
85C2×C59⋊C8—42no—
86C2×C59⋊C8—41no—
87C2×C59⋊C8C22⋊C414yes—
88C23×C59C4×D411yescharacteristic
89Q8×C59—44no—
90Q8×C59—82no—
91C2×C4×C59—22no—
92C2×C4×C59—22no—
93C2×C4×C59—42no—
94C2×C4×C59—82no—
95C2×C4×C59C2×C22⋊C411yescharacteristic
96C2×C4×C59C4×D411yescharacteristic
97C2×C4×C59#12111yescharacteristic
98C2×C4×C59#12111yescharacteristic
99C2×C4×C59#12411yescharacteristic
100C2×C4×C59#12711yescharacteristic
101C2×C4×C59#13712yes—
102C2×C4×C59#13712yes—
103C2×Dic59—42no—
104C2×Dic59—82no—
105Dic118—82no—
106Dic118—82no—
107C8×C59—42no—
108C8×C59—81no—
109C59⋊C8—24no—
110C59⋊C8—42no—
111C59⋊C8—81no—
112#9803—591nomaximal, Sylow
113C22×C59—21no—
114C22×C59—21no—
115C22×C59#39011yescharacteristic
116C22×C59#44112yes—
117C4×C59—21no—
118C4×C59—21no—
119C4×C59—82no—
120C4×C59#41312yes—
121C4×C59#47012yes—
122C4×C59#47112yes—
123C4×C59#49711yescharacteristic
124C4×C59#49711yescharacteristic
125Dic59—82no—
126C2×#487—591no—
127#1997—591no—
128#1997D5911yescharacteristic
129#1566—591no—
130#1549—591no—
131#1548—591no—
132#1451—591no—
133C2×C59—22no—
134C2×C59#196711yescharacteristic
135C2×C59#197111yescharacteristic
136C2×C59#197711yescharacteristic
137C2×C4⋊Q8—591no—
138C2×C4⋊Q8C2×D5911yescharacteristic
139#487—1182no—
140#487—1182no—
141#431—591no—
142#423—591no—
143#423C2×D5911yescharacteristic
144C2×#103—594no—
145C4×M16C2×D5911yescharacteristic
146C2×C4×C8—591no—
147#343—22no—
148#343—1182no—
149#334—1182no—
150#333—1182no—
151#332—1182no—
152#322—1182no—
153C59#980311yescharacteristic, complemented, Sylow
154C22×Q8—1181no—
155C22×Q8C4×D5912yes—
156C2×M16—21no—
157C2×M16—1181no—
158C2×M16C22⋊D5912yes—
159C22×C8—592no—
160C4⋊Q8—21no—
161C4⋊Q8—21no—
162C4⋊Q8—21no—
163C4⋊Q8—21no—
164C4⋊Q8—1181no—
165C4⋊Q8—1181no—
166C4⋊Q8—1181no—
167C4⋊Q8—1181no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—592no—
171C2×C4⋊C4—1181no—
172C2×C42C22×D5911yescharacteristic
173C4⋊C8—21no—
174C4⋊C8—21no—
175C4⋊C8—592no—
176C4⋊C8—1181no—
177C4⋊C8—1181no—
178#103—1188no—
179C22⋊C8—1181no—
180#97—21no—
181C4×C8—21no—
182C4×C8—592no—
183C4×C8—592no—
184C4×C8—1181no—
185C2×Q8—22no—
186C2×Q8—22no—
187C2×Q8—44no—
188C2×Q8—4722no—
189C2×Q8—2361no—
190C2×Q8—2361no—
191C22×C4—22no—
192C22×C4—1182no—
193C22×C4C2×C4×D5911yescharacteristic
194C22×C4#1174568511yescharacteristic
195C22×C4C2×C22⋊D5911yescharacteristic
196M16—22no—
197M16—22no—
198M16—42no—
199M16—2362no—
200C2×C8—22no—
201C2×C8—41no—
202C2×C8—594no—
203C2×C8—1182no—
204C2×C8—2362no—
205C2×C8—2361no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—1182no—
211C4⋊C4—1182no—
212C4⋊C4—2361no—
213C4⋊C4—2361no—
214C42D4×D5911yescharacteristic
215C42D4×D5911yescharacteristic
216C42D4×D5911yescharacteristic
217C42#1174568711yescharacteristic
218C23C4×C22⋊D5911yescharacteristic
219Q8—44no—
220Q8—82no—
221Q8—4722no—
222Q8—4722no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—82no—
227C2×C4—4722no—
228C2×C4—2362no—
229C2×C4C22⋊C4×D5911yescharacteristic
230C2×C4(C22⋊D59)⋊C411yescharacteristic
231C2×C4#1427369911yescharacteristic
232C2×C4#1427370011yescharacteristic
233C2×C4#1427371311yescharacteristic
234C2×C4#1427372311yescharacteristic
235C2×C4#1427375712yes—
236C2×C4#1427375812yes—
237C8—42no—
238C8—81no—
239C8—1184no—
240C8—4721no—
241C8—2362no—
242C22—21no—
243C22—21no—
244C22#1683730211yescharacteristic
245C22#1683750712yes—
246C4—21no—
247C4—21no—
248C4—82no—
249C4—4722no—
250C4#1683738312yes—
251C4#1683765812yes—
252C4#1683766812yes—
253C4#1683779411yescharacteristic
254C4#1683779711yescharacteristic
255C2—22no—
256C2#2142494211yescharacteristic
257C2#2142496611yescharacteristic
258C2#2142500011yescharacteristic
subgroupG/H
centerC22#16837302
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1997C2
socleC22×C59#390
prime radicalC23×C59C4×D4
cosocleC2×C42×C59C23
hypercenter#1997D59
hypocenterC59#9803
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
153. C59#9803semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#168377522
#214250852
#214228512
#214227822
#214227772
#214223832
C59×#19972
#980359